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Lyman- a quasar spectra as cosmological probes. MATTEO VIEL. INAF & INFN – Trieste. THEORY: GAS in a L CDM universe. 80 % of the baryons at z=3 are in the Lyman- a forest. Bi & Davidsen (1997), Rauch (1998). baryons as tracer of the dark matter density field - PowerPoint PPT Presentation
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Lyman- quasar spectra as cosmological probes
MATTEO VIEL
INAF & INFN – Trieste
80 % of the baryons at z=3 are in the Lyman- forest
baryons as tracer of the dark matter density field
IGM ~ DM at scales larger than the
Jeans length ~ 1 com Mpc
flux = exp(- ~ exp(-(IGM )1.6 T -0.7 )
THEORY: GAS in a CDM universe
Bi & Davidsen (1997), Rauch (1998)
DATA: high resolution spectrum
Outline
- Where we were
- What data we got
- How we used them
- What we achieved
- Where we are going
Mini historical background
The data sets
Theoretical framework
Results
Perspectives
Linear matter power spectrum
Mini historical background
1965: Bahcall & Salpeter, Gunn & Peterson. First extimates of IGM opacity. HI in clusters?1971: A forest of lines seen by Lynds80’s: models of the IGM (gravitational or pressure confinements of clouds)90’s: CDM + median fluctuated IGM (Bi, McGill…) semianalytical models + Hydro sim.
Croft, Weinberg and co-workers (98,99,02): the effective bias method
PF (k) = b2(k) P(k)
28% uncertainty in the power spectrum amplitude
Recovered in velocity space
GOAL: the primordial dark matter power spectrum from the observed flux spectrum
Tegmark & Zaldarriaga 2002
CMB physics z = 1100 dynamics
Lyphysics z < 6 dynamics + termodynamics
CMB + Lyman Long lever arm
Constrain spectral index and shape
Relation: P FLUX (k) - P MATTER (k) ??
Continuum fitting
Temperature, metals, noise
The data sets
The Croft et al. (02) sample: 53 QSO spectra (30 at high res from Keck and 23 low.res)
Tytler et al. (04): 77 low resolution low S/N spectra (KAST spectrograph) at <z>=1.9
The LUQAS sample: Large Uves Quasar Absorption Spectra part of the ESO Large programme by J. Bergeron – 27 high.res and high S/N spectra at <z>=2.125 -- Kim et al. (2004)
The SDSS QSOs (release 1&2): 3300 low. resolution and low S/N QSO spectra z=2.2-4.2. McDonald et al. (2005)
Becker et al. (07) sample: 55 high.res. Spectra spanning z=2-6.4
There is a lot of astrophysics (reionization, metal enrichment, UV background etc.) as well…
3035 LOW RESOLUTION LOW S/N vs 30 HIGH RESOLUTION HIGH S/NSDSS LUQAS
SDSS vs LUQAS
McDonald et al. 2005 Kim, MV et al. 2004
The data sets-II
The data sets: the flux power -III
Main systematics:
continuum fitting + metal contamination + meanflux level determination
McDonald et al. 05SDSS
Viel, Hahnelt & Springel 04
z=2.2
z=4.2
Viel et al. 08
The interpretation: bias method - I
1. LUQAS sample analysed with the effective bias method
Viel, Haehnelt & Springel 04
DER
IVED
LIN
EA
R D
AR
K M
ATTER
PO
WER
SPE
CTR
UM z=2.125 z=2.72
2 likelihood code distributed with COSMOMC
2. SDSS power analysed by forward modelling motivated by the huge amount of data with small statistical errors
+ +
CMB: Spergel et al. (05) Galaxy P(k): Sanchez & Cole (07) Flux Power: McDonald (05)
Cosmological parameters + e.g. bias + Parameters describing IGM physics
132 data points
The interpretation: full grid of sims - II
- Cosmology
- Cosmology
- Mean flux
- T=T0 (1+)-1
- Reionization
- Metals
- Noise- Resolution
- Damped Systems
- Physics- UV background
- Small scales
Tens of thousands of modelsMonte Carlo Markov Chains
McDonald et al. 05The interpretation: full grid of sims - IIb
McDonald et al. 05: fine grid of (calibrated) HPM (quick) simulationsViel & Haehnelt 06: interpolate sparse grid of full hydrodynamical (slow) simulations
Both methods have drawbacks and advantages:
1- McDonald et al. 05 better sample the parameter space2- Viel & Haehnelt 06 rely on hydro simulations, but probably error bars are underestimated
The flux power spectrum is a smooth function of k and z
P F (k, z; p) = P F (k, z; p0) + i=1,N P F (k, z; pi) (pi - pi0)
pi
p = p0
Best fit
Flux power
p: astrophysical and cosmological parameters
but even resolution and/or box size effects if you want to save CPU time
The interpretation: flux derivatives - III
3. Independent analysis of SDSS power
RESULTS
POWER SPECTRUM AND NEUTRINOS
Results Lyman- only with full grid: amplitude and slope
McDonald et al. 05
Croft et al. 98,02 40% uncertaintyCroft et al. 02 28% uncertaintyViel et al. 04 29% uncertaintyMcDonald et al. 05 14% uncertainty
2 likelihood code distributed with COSMOMC
SDSS data only
8 = 0.91 ± 0.07n = 0.97 ± 0.04
Fitting SDSS data with GADGET-2 this is SDSS Ly- only !!
FLUX DERIVATIVES
Results Lyman- only with flux derivatives: correlations
Summary (highlights) of results
1. Tightest constraints to date on neutrino masses and running of the spectral index Seljak, Slosar, McDonald JCAP (2006) 10 014
2. Tightest constraints to date on the coldness of cold dark matter
MV et al., Phys.Rev.Lett. 100 (2008) 041304
Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11
VHS-LUQAS: high res Ly-a from (Viel, Haehnelt, Springel 2004)SDSS-d: re-analysis of low res data SDSS (Viel & Haehnelt 2006)WL: COSMOS-3D survey Weak Lensing (Massey et al. 2007) 1.64 sq degree public available weak lensing COSMOMC module
Lyman- forest + Weak Lensing + WMAP 3yrs
VHS+WMAP1
AM
PLIT
UD
E
SPECTRAL INDEXMATTER DENSITY
http://www.astro.caltech.edu/~rjm/cosmos/cosmomc/
Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11
Lyman- forest + Weak Lensing + WMAP 3yrs
WMAP5only Dunkley et al. 088 = 0.796 ± 0.036ns = 0.963 ± 0.015m= 0.258 ± 0.030h = 71.9 ± 2.7= 0.087 ± 0.017dn/dlnk= -0.037 ± 0.028
WMAP5+BAO+SN Komatsu et al. 08
8 = 0.817 ± 0.026ns = 0.960 ± 0.014h = 70.1 ± 1.3 = 0.084 ± 0.016
with Lyman- factor 2 improvements onthe running
|dn/dlnk| < 0.021
WMAP 5yrs
Lesgourgues & Pastor Phys.Rept. 2006, 429, 307
Lyman-forest
m = 0.138 eV
m = 1.38 eV
Active neutrinos - I
Active neutrinos - II Seljak, Slosar, McDonald, 2006, JCAP, 0610, 014
m (eV) < 0.17 (95 %C.L.) r < 0.22 (95 % C.L.)
running = -0.015 ± 0.012 Neff = 5.2 (3.2 without Ly) CMB + SN + SDSS gal+ SDSS Ly-
normal
inverted
1
2
31,2
3
Goobar et al. 06 get upper limits 2-3 times larger…… for forecasting see Gratton, Lewis, Efstathiou 2007
Tight constraints because dataare marginally compatible
2 limit
RESULTS
WARM DARK MATTER Or if you prefer.. How cold is cold dark matter?
Lyman- and Warm Dark Matter - I
CDMWDM 0.5 keV
30 comoving Mpc/h z=3
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
k FS ~ 5 Tv/Tx (m x/1keV) Mpc-1
In general
Set by relativistic degrees of freedom at decoupling
See Colombi, Dodelson, Widrow, 1996 Colin, Avila-Reese, Valenzuela 2000 Bode, Ostriker, Turok 2001 Abazajian, Fuller, Patel 2001 Wang & White 2007 Colin, Avila-Reese, Valenzuela 2008
Lyman- and Warm Dark Matter - II
CDM
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
[P (k) WDM/P (k) CDM ]1/2
P(k) = A kn T2 (k)
T x 10.75 =T g (T D)
1/3
1/3
Light gravitino contributing to a fraction of dark matter
Warm dark matter
10 eV
100 eV
MV et al., Phys.Rev.Lett. 100 (2008) 041304
Tightest constraints on mass ofWDM particles to date:
m WDM > 4 keV (early decoupled thermal relics)
m sterile > 28 keV (standard Dodelson-Widrow mechanism)
SDSS + HIRES data
(SDSS still very constraining!)
SDSS range Completely new small scale regime
Lyman- and Warm Dark Matter - III
COLD (a bit) WARM sterile 10 keV
Little room for standard warm dark matter scenarios…… … the cosmic web is likely to be quite “cold”
NEW RESULTS forSIMPLER STATISTICS ?
Fitting the flux probability distribution function
Bolton, MV, Kim, Haehnelt, Carswell (08)
T=T0(1+) -1
Flux probabilitydistributionfunction
Invertedequation of state <1 means voids arehotter than mean density regions
Fitting the flux probability distribution function-II
Bolton, MV, Kim, Haehnelt, Carswell (08)
SUMMARY- Lyman- forest is an important cosmological probe at a unique range of scales and redshifts
- Current limitations are theoretical (more reliable simulations are needed for example for neutrino species) and statistical errors are smaller than systematic ones
- Need to fit all the IGM statistics at once (mean flux + flux pdf + flux power + flux bispectrum + … ) -Tension with the CMB is partly lifted (8 went a bit up). Still very constraining for what happens at those scales:
running (inflation), neutrinos, warm dark matter candidates …
SYSTEMATICS
Systematics I: Mean flux
Effective optical depth
<F> = exp (- eff) Power spectrum of F/<F>
Low resolution SDSS like spectra
High resolution UVES like spectra
Systematics II: Thermal state
T = T0 ( 1 + )
Statistical SDSS errors on flux power
Thermal histories Flux power fractional differences
Gnedin & Hui 1998
equation of motion for gas element
if T = T0 ( 1 + )
Other similar techniques agree with the statement aboveMeiksin & White 2001
Systematics III: Numerical modelling HPM simulations
Systematics IV: Numerical modelling HPM simulations
Full hydro 200^3 part. HPM NGRID=600 HPM NGRID=400F
LUX
PO
WE
R
MV, Haehnelt, Springel (2006)
UV fluctuations from Lyman Break Galaxies Metal contribution
Systematics V: UV fluctuations and Metals
McDonald, Seljak, Cen, Ostriker 2004 Kim, MV, Haehnelt, Carswell, Cristiani (2004)
Ratio of Flux power Ratio of Flux power
m WDM > 550 eV thermal > 2keV sterile neutrino
WDM CWDM(gravitinos)
neutrinos
Lyman- and Warm Dark Matter - IV
Viel et al. (2005)from high-resz=2.1 sample
Seljak, Makarov, McDonald, Trac, PhysRevLett, 2006, 97, 191303
m WDM > 1.5-2 keV thermal > 10-14 keV sterile neutrino
MATTER FLUX
FLUX FLUX
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PhysRevLett, 2006, 97, 071301
Active neutrinos -II
m (eV) < 1 eV (95 % C.L.) WMAP1 + 2dF + LY
WDM neutrinos
Good agreement with the latest Tegmark et al. results…..
Fitting the mean flux evolution –I
Faucher-Giguere et al. (07)
McDonald et al. (05)
Lyman- and Warm Dark Matter - III
WDM 0.5 keV
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
WARM DARK MATTER (light) GRAVITINO
sets the transition scale f x is x/
DM
m < 16 eV (2)
SUSY < 260 TeV